Stability analysis of delay difference systems

For quadratic delay difference systems, a result related to stability analysis is established. More specifically, the zero solution is uniformly stable and uniformly asymptotically stable for suitably small delay r < r*, where r* is the admissible maximum value of delay under certain conditions; furthermore, the estimates of the corresponding stability and asymptotic stability regions are given. Hence, the obtained result is both qualitative and quantitative. Also, as a by-product, an improved uniform asymptotic stability criterion is established.